The farm was a metaphor. As for productivity, often we tend to claim that productivity has been maximized in a manner that is a bit, myopic. As per the wikipedia article on productivity: "
Productivity is the
efficiency of
production of
goods or
services expressed by some measure. Measurements of productivity are often expressed as a ratio of an aggregate
output to a single
input or an aggregate input used in a production process, i.e. output per unit of input, typically over a specific period of time." And herein lies the problem. Let's examine agriculture, for an example case to explore. So you produce wheat, and you have determined that you can increase wheat productivity (in terms of bushels per acre) by concentrating farmland in one area (like big AG today tends to do).
Now, prior to the use of fossil fuels, this mode of production would actually have been considered to be less efficient systemically (due to high transportation costs) when compared to dispersed, local farms with low transportation and distribution costs. Things can get a bit murky here, so let's use our input here as calories expended per bushel of wheat produced. To the farmer, the cost they personally see in terms of currency has indeed come down, but do they count the calories of energy expended through the use of fossil fuels in their equation? What if, we are actually expending more calories per bushel of wheat than we were in the Medieval period, but those calories are simply extracted from liquid and gas "batteries" if you will. Human metabolism burns calories at a fraction that combustion of fossil fuels can, because this energy is highly concentrated in fossil fuels. It would take many human hours of labor to do the equivalent work of a liter of gasoline. (the number I found is that 1 gallon of gas is close to 29,000 calories of energy). For contrast, a Medieval serf was estimated to have burned around 4,000 calories per day on the farm. So, one gallon of gas can do roughly the same amount of work (assuming perfect engineering of the products to reduce the loss of calories as heat), as about 7 serfs working full days.
Now, I could dig up a lot of information to actually figure out if we are expending more calories per bushel of wheat than in the past, but I may not need to if one considers that, not only do we need calories to be expended on the farm, we also need them to be expended on the transportation and distribution networks, as well as the fossil fuel industry, and refrigeration and storage industries to name a few accessory industries. How many calories is the system now spending on the production of one bushel of wheat vs the past? One may think it should be less if prices are low, but there are other ways of keeping prices low in the face of energy expenditure, and fossil fuel extraction is one way of doing so. Hiding overall costs in other industries is another. For example, calories end up getting spent on the healthcare industry as food become less nutritionally dense and hold pesticide residues, etc, and we consume those things as dietary staples. Yes, the hunter-gatherer needed more land to do their thing, but as far as calories expended per unit of nutrition one would be hard pressed to argue that their societies demanded as much energy use as ours to remain functional. Bear in mind I am not advocating for primitivism here, as the primitivist ultimately loses the moment someone decides not to be primitive, thereby making it a utopian system. To state what I am trying to say more simply: complexity usually requires more energy expenditure.
As for you contention about cattle not being able to survive independently, well, if that were true, they would not have been around to for us to domesticate them, for they would have gone extinct. If you are actually claiming that the survival rate of individual cattle is better with us around, well, absent human intervention, their average lifespans are from 20-25 years before dying of old age. In our modern system, they can expect to live around 5 years or so, but we do breed them, so they do persist and survive until the age of reproduction. They'll survive until the age of reproduction with human stewards, but they would still do so in concentrations that are sufficient for survival without us.
Overshoot, which is the phenomenon you speak of, can happen. Humans have even done this before (or so the evidence suggests) in certain pockets, see Easter Island, for example. Usually, when the carrying capacity of a given area is exceeded, populations can collapse, but extinction is not guaranteed so long as some hard to reach resources remain, and the renewable food sources are allowed to propagate.
And actually, if one is applying the concept of creating an island paradise for humans to humans, one would need accurate information on whether this can actually be achieved in the first place (and if so, how to do it), a moral imperative (ethical justification) or farsighted self-interest (who could ever trust a farmer (not a literal farmer), after all, and pre-emptive survival for self-interest would involve eliminating competitors and creating docile peers who represent no threat to you) to do so, and they would need a practical plan of action which would involve handling the opponents of such an action who would inevitably spring up when their personal interests are threatened by the elevating of the interests of others, and the larger system as whole. Conversely, the farmer does not need to have a single philosophical thought as a prerequisite for doing what they do (they simply only need to blindly follow their urge for growth). If one discovered the open pature to improve the life of the cattle, one would be hard pressed to convince the farmer through reason to give up some of their productivity gains in exchange for improving the wellbeing of the cattle. Psychology would also claim that humans tend to "feel" losses greater in magnitude than they "feel" gains, assuming one could actually measure the magnitude of an emotion.
